Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Solution:-

Let,

      Larger angle = x

      Smaller angle = y

Case (i): The larger angle exceeds the smaller angle by 18 degrees,

   ∴ x = y + 18°       ------- (i)

Case (ii): We know that, the sum of the measures of angles of a supplementary pair is always 180°,

   ∴ Sum of both angles = 180°

   ∴ x + y = 180°

   ∴ y + 18° + y = 180°       { from (i) }

   ∴ y + y = 180° - 18°

   ∴ 2y = 162°

   ∴ y =

162° / 2

   ∴ y = 81°

➙ Putting y = 81° in Eqⁿ(i)

   ∴ x = 81° + 18°

   ∴ x = 99°

Therefore,

      Larger angle = x = 99°

      Smaller angle = y = 81°

Hence,

          The larger and smaller angles are 99° and 81° respectively.

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Try This..

✒ Find two supplementary angles such that one is twice the other.

✒ One angle is 20° less than its supplement. What are the angles?

✒ Two angles are supplementary. If one angle is three times the other, find them.

✒ The difference between two supplementary angles is 30°. Find the angles.

❌ Common Mistakes

Forgetting the sum of supplementary angles is always 180°:

▸ Always remember; supplementary angles add up to 180°, not 90° (that’s complementary!).

Wrong variable assignments:

▸ Clearly define what each variable stands for; smaller vs. larger angle.

Algebraic errors while solving:

▸ Keep your algebra steps clean and double-check calculations.

Skipping the verification step:

▸ Always add the final angles to see if they make 180°. This builds confidence and avoids careless mistakes.

📝 Related Questions:-

• Ex 3.2 Q2 - Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.
• Ex 3.2 Q3 (i) - The difference between two numbers is 26 and one number is three times the other. Find them.
• Ex 3.2 Q3 (iii) - The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
• Ex 3.2 Q3 (iv) - The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
• Ex 3.2 Q3 (v) - A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
• Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Queries Solved:-

Class 10 Ex 3.2

Ex 3.2 Q3 ii Class 10

Class 10 Ex 3.2 Q3 ii

Class 10 Chap 3 Ex 3.2 Q3 ii

Class 10 Pair Of Linear Equations in Two Variables

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